### Abstract

The force response of activated striated muscle to length perturbations includes the so-called C-process, which has been considered the frequency domain representation of the fast single-exponential force decay after a length step (phases 1 and 2). The underlying molecular mechanisms of this phenomenon, however, are still the subject of various hypotheses. In this study, we derived analytical expressions and created a corresponding computer model to describe the consequences of independent acto-myosin cross-bridges characterized solely by 1), intermittent periods of attachment (t_{att}) and detachment (t_{det}), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (k _{stiff}) effective only during periods of attachment. The computer-simulated force response of 20,000 (N) cross-bridges making up a half-sarcomere (F_{hs}(t)) to sinusoidal length perturbations (L _{hs}(t)) was predicted by the analytical expression in the frequency domain, (F̃_{hs}(ω)/L̃_{hs}(ω)) = (t̄_{att}/t̄_{cycle})Nk̄_{stiff}(iω /(t̄_{att}^{-1} + iω)); where t̄_{att} = mean value of t_{att}, t̄_{cycle} = mean value of t _{att} + t_{det}, k̄_{stiff} = mean stiffness, and ω = 2π x frequency of perturbation. The simulated force response due to a length step (L_{hs}) was furthermore predicted by the analytical expression in the time domain, F_{hs}(t) = (t̄_{att}/ t̄_{cycle})Nk̄_{stiff}L_{hs} e ^{-t/t̄att}. The forms of these analytically derived expressions are consistent with expressions historically used to describe these specific characteristics of a force response and suggest that the cycling of acto-myosin cross-bridges and their associated stiffnesses are responsible for the C-process and for phases 1 and 2. The rate constant 2πc, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to t̄_{att}^{-1}. Experimental results from activated cardiac muscle examined at different temperatures and containing predominately α- or β-myosin heavy chain isoforms were found to be consistent with the above interpretation.

Original language | English (US) |
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Pages (from-to) | 760-769 |

Number of pages | 10 |

Journal | Biophysical journal |

Volume | 93 |

Issue number | 3 |

DOIs | |

State | Published - Aug 2007 |

Externally published | Yes |

### ASJC Scopus subject areas

- Biophysics

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## Cite this

*Biophysical journal*,

*93*(3), 760-769. https://doi.org/10.1529/biophysj.106.101626